Abstract
Multiscale models possess the potential to uncover new insights into infectious diseases. Here, a rigorous stability analysis of a multiscale model within-host and between-host is presented. The within-host model describes viral replication and the respective immune response while disease transmission is represented by a susceptible-infected model. The bridging of scales from within- to between-host considered transmission as a function of the viral load. Consequently, stability and bifurcation analyses were developed coupling the two basic reproduction numbers [Formula: see text] and [Formula: see text] for the within- and the between-host subsystems, respectively. Local stability results for each subsystem, including a unique stable equilibrium point, recapitulate classical approaches to infection and epidemic control. Using a Lyapunov function, global stability of the between-host system was obtained. Our main result was the derivation of the [Formula: see text] as an increasing function of [Formula: see text]. Numerical analyses reveal that a Michaelis-Menten form based on the virus is more likely to recapitulate the behavior between the scales than a form directly proportional to the virus. Our work contributes basic understandings of the two models and casts light on the potential effects of the coupling function on linking the two scales.
Highlights
Infectious diseases remain a global concern despite the advance of medicine and living conditions [28]
We focused on dynamics of virus (V ) and T-cell populations (E) as follows [4]:
It is useful to describe the dynamics of both systems (1) and (22) with respect to a single basic reproduction number
Summary
Infectious diseases remain a global concern despite the advance of medicine and living conditions [28]. Infectious diseases dynamics, are governed by many interconnected scales, from complex within-host infection processes, to between hosts, vectors, and environments. In this context, mathematical modelling is an essential tool to untangle the processes, providing understandings of diseases dynamics and public health policies [17]. Typical infectious diseases models [9,25] restrict their dynamics to one of the two scales: within-host, focusing on cellular interactions; and between-host, focusing on transmission and infection statuses (Figure 1). Results of analytical analyses are accompanied by phase portraits and bifurcation diagrams
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